In gear drive engineering the efforts to increase the power concentration and reduce noise emission of the gear units are leading more and more to gears units and individual gears with three-dimensionally, i.e. topologically modified tooth flanks. Thanks to such modifications, favourable tooth bearing and dynamic response behaviour of gear pairs in mesh can be achieved, although their tooth deformation alters under the variable loading. As a result of these efforts, gears are calculated, designed and manufactured which are provided with complex tooth flank modifications, e.g. in the form of tip and root relief, or of undulations which run parallel to the lines of contact of a gear pair.
With the familiar methods and tools applied in generation grinding with a cylindrical grinding worm, workpieces with such tooth flank modifications can only be produced within limits, i.e. with considerable residual deviations or very extensive profiling resources.
In EP-A-0′278′512 a cylindrical grinding worm is described with a pressure angle varying across the grinding worm width. This grinding worm permits the generation of spur and helical gears with crowned tooth flanks with or without bias. A disadvantage of this solution is the residual deviations that occur due to the arc shaped locus of the path of contact between grinding worm and workpiece tooth flank in conjugate reproduction. A further disadvantage is the small number of workpieces that can be ground per grinding worm profiling operation. For since the modified grinding worm zone is used both for rough and for finish grinding, the high wear suffered during rough grinding has a negative effect on the ultimate accuracy.
The last mentioned disadvantage is avoided in DE-A-197'06'867.7 (FIG. 1) in that the grinding worm is divided into several zones across its width, which are used separately for rough grinding and finish grinding. The grinding worm is profiled with a profile roll. On account of the given fixed profile of the profile roll, however, a considerable loss in usable grinding worm width is incurred at the transition between the rough and the finish grinding zone. The reasons for this are explained later in the text in more detail with reference to the FIGS. 1 to 2a. 
DE-A-196'24'842 A1 and WO 95/24989 describe the generation of grinding worm profiles with radiussed form rolls, with which it is possible by continuous path control to produce practically any desired grinding worm thread profile. The disadvantage of these solutions lies chiefly in the necessarily long profiling times, so that they may be suitable for small and medium series, but not for large series production.
Also known is the production of cylindrical convex and concave crowning and globoidal geometry on worm type and gear type grinding tools with internal and external teeth, using an abrasive grain coated profiling gear. The grinding worm flank geometry derives from the conjugate reproduction of the tooth geometry of the profiling gear which, instead of the workpiece, is brought into mesh with the grinding worm, and of which the tooth geometry corresponds with that of the workpiece. A three-dimensionally modified grinding worm geometry can therefore also be produced by the diagonal generation profiling method, using an accordingly topologically modified profiling gear.
One of the disadvantages of profiling a grinding worm with a profiling gear lies in the fact that when manufacturing the workpieces the workpiece flank geometry can only be altered slightly or not at all. The reason for this is that once the relevant profiling gear is made, its geometry can only be altered slightly or not at all. This disadvantage and the high cost of a profiling gear makes the profiling of a grinding worm with a profiling gear only economical in large series production, where the desired workpiece geometry remains constant over long manufacturing periods, and the long life of an abrasive coated profiling gear can be fully exploited.